Answer
$\dfrac{5\sqrt{6}}{6}$
Work Step by Step
Using the properties of radicals, the given expression, $
\dfrac{5\sqrt{2}}{2\sqrt{3}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{5\sqrt{2}}{2\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}
\\\\=
\dfrac{5\sqrt{6}}{2\cdot3}
\\\\=
\dfrac{5\sqrt{6}}{6}
.\end{array}
